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04-BS-5: December 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Power Series Solution of a Linear ODE
  2. Question 2 Fourier Series and Term-by-Term Differentiation
  3. Question 3 Fourier Transform of a Triangular Pulse
  4. Question 4 Least-Squares Parabola Proof and Lagrange Interpolation
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Bisection, a Second-Order Iterative Method, and Fixed-Point Iteration
  7. Question 7 Cholesky-Type Factorization of a Symmetric Positive-Definite Matrix

Start with Question 1 →

National Examinations, December 2016 — 04-BS-5 Advanced Mathematics, 3 hours, closed book (one double-sided aid sheet permitted). Any five of the seven questions constitute a complete paper; all seven are answered below as a full study resource.

Reference texts: Kreyszig, Advanced Engineering Mathematics, 10th ed. (Wiley) — Ch. 5 (Power Series Solutions of ODEs), Ch. 11 (Fourier Series and Transforms), Ch. 19 (Interpolation, Curve Fitting, Numerical Integration, Solution of Equations by Iteration), Ch. 20 (Numerical Linear Algebra / Cholesky Factorization).